两输入两输出系统回路时滞裕度的频域计算方法

Computation of TimeDelay Margins for Two Input Two Output Systems in Frequency Domain

为更加方便准确地得到时滞裕度,针对两输入两输出系统提出回路时滞裕度的频域计算方法。通过求解规则几何图形的交点计算时滞稳定边界,利用范数不等式给出频率范围估算方法,从而减小计算量;在估计区域内计算所有时滞稳定边界,通过作图确定时滞裕度。仿真算例表明,该方法计算简便,同时适用于时滞系统和高阶系统时滞裕度的确定。

This paper presents a computation method of time delay margin for two-input two-output(TITO)systems.The time delay stability boundaries are obtained by calculating the intersection points of the regular geometric figures.The frequency range is estimated based on the matrix norm inequality method,which helps to reduce the computation burden.The time delay margin is finally determined by drawing the figures.Simulations demonstrate that the proposed method is effective for both time delay systems and high order systems.